Recently, the work [1]} proposes the Stochastic Gradient Variational Bayes (SGVB) estimator and Auto-encoded Variational Bayes (AEVB) algorithm. One popular technique under this framework is Variational Auto-Encoder (VAE). By using neural network for parameterizing a flexible inference model \(q_{\phi }(\mathbf {z}|\mathbf {x})\)  to approximate posterior \(p_{\theta _{}}(\mathbf {z}|\mathbf {x})\) , along with the reparameterization trick, the lower bound \(\mathcal {L}\)  of marginal likelihood is differentiable. In consequence, the model can be effectively trained. To a certain extent, the AEVB algorithm liberates the limitations when devising complex probabilistic generative models, especially for deep generative models.
